Problem: Solve for $X$. $X+\left[\begin{array}{rr}2 & -2 & 6 \\ -8 & 17 & 9 \end{array}\right]=\left[\begin{array}{rr}-13 & 24 & 24 \\ 24 & 13 & 12\end{array}\right] $ $X=$
Explanation: The Strategy First, we can represent the matrices of the equation with letters, which will make the equation easier to handle. Then we can solve the equation for $X$ and obtain an expression with the letters we defined. Finally, we can substitute back the actual matrices into the resulting expression and simplify it. Solving the equation for $X$ We are given the following equation. $X+\left[\begin{array}{rr}2 & -2 & 6 \\ -8 & 17 & 9 \end{array}\right]=\left[\begin{array}{rr}-13 & 24 & 24 \\ 24 & 13 & 12\end{array}\right] $ Let's represent the above matrices as follows. $A=\left[\begin{array}{rr}2 & -2 & 6 \\ -8 & 17 & 9 \end{array}\right] ~~~~~~~~~ B = \left[\begin{array}{rr}-13 & 24 & 24 \\ 24 & 13 & 12\end{array}\right]$ Then we can rewrite the equation as follows. $X+A=B$ Now it's simple to solve the equation for $X$. $\begin{aligned}X+A&=B\\\\ X&=B-A \end{aligned}$ Finding $X$ We found that $X=B-A$. Now we can substitute the actual matrices back into the expression and simplify. $\begin{aligned}X&=B-A \\\\&=\left[\begin{array}{rr}-13 & 24 & 24 \\ 24 & 13 & 12\end{array}\right]-\left[\begin{array}{rr}2 & -2 & 6 \\ -8 & 17 & 9 \end{array}\right] \\\\\\&=\left[\begin{array}{rr}(-13-2) & (24+2) & (24-6) \\ (24+8) & (13-17) & (12-9)\end{array}\right] \\\\\\&=\left[\begin{array}{rr}-15 & 26 & 18 \\ 32 & -4 & 3\end{array}\right]\end{aligned}$ Summary $X=\left[\begin{array}{rr}-15 & 26 & 18 \\ 32 & -4 & 3\end{array}\right]$